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larisa86 [58]
3 years ago
6

Please answer the Scientific Notation Question! And if you can, please also generously explain. Your help is greatly appreciated

!

Mathematics
1 answer:
Ugo [173]3 years ago
8 0

Convert the fraction to a decimal by dividing the numerator by the denominator.

1.05*10^-10

so a is the answer

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Item 5<br> Write 77.5% as a fraction or mixed number in simplest form.
jeyben [28]

<span>77.5% can also be written as 77.5/100, but if you're the mathematical notation police, people don't like decimals on a fraction, sooo, an equivalent form is: </span>

<span>
 = (77.5)/(100) * (2/2)
= 155/200
= 31/40
= 0 31/40 </span>

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2 years ago
In 20 minutes a heart can beat 700 times. At this rate in how many minutes will a heart beat 140 times at what rate can a heart
murzikaleks [220]
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3 years ago
Find the sum of (4x^3+2x) + (8x^3+4)
Savatey [412]
The answer would be 12x^3+ 2x + 4
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3 years ago
Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions
monitta
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take z=y', so that z'=y'' and we're left with the ODE linear in z:

y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2

Now suppose y has a power series expansion

y=\displaystyle\sum_{n\ge0}a_nx^n
\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}
\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}

Then the ODE can be written as

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0

\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0

\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0

All the coefficients of the series vanish, and setting x=0 in the power series forms for y and y' tell us that y(0)=a_0 and y'(0)=a_1, so we get the recurrence

\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}

We can solve explicitly for a_n quite easily:

a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}

and so on. Continuing in this way we end up with

a_n=\dfrac{a_1}{n!}

so that the solution to the ODE is

y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x

We also require the solution to satisfy y(0)=a_0, which we can do easily by adding and subtracting a constant as needed:

y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}
4 0
3 years ago
Write in simplest radical form: √208
Arte-miy333 [17]

208:2=104\\104:2=52\\52:2=26\\26:2=13\\13:13=1\\\\208=2\cdot2\cdot2\cdot2\cdot13=2^2\cdot2^2\cdot13\\\\\sqrt{208}=\sqrt{2^2\cdot2^2\cdot13}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{13}=2\cdot2\cdot\sqrt{13}=4\sqrt{13}\\\\Answer:\ \sqrt{208}=4\sqrt{13}\\\\Used:\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a

6 0
3 years ago
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